So the "not" we place before the gerund or infinitive is an
exception?(no operators are found in the 2 examples you've given to me)
Yes. These are exceptions. There's no operator, but you place not before the gerund or infinitive.
and does the infinitive you mentioned include both to-infinitive and bare-infinitive?
No. Just the to infinitive.
if the answer of the 2nd question is yes, why isn't "I not yet see sth." correct?
it It is "not + bare infinitive",
doesn't isn't it?
No. It's not an infinitive.
or it's because "see" is used as verb in this sentence, but not infinitive?
Yes. see is the main verb -- present tense, not infinitive.
Bare infinitives occur after operators most of the time, so this situation is covered by the other rules. (I cannot see anything yet. - Here can is the main verb, and an operator. see is a bare infinitive. There's already a rule to place not after the operator can, so another rule to place not before the bare infinitive is totally unnecessary.)
CJ